\u00dc\u00e7 y\u00fcz elli y\u0131l boyunca \u00e7\u00f6z\u00fclmemi\u015f Fermat\u2019\u0131n Son Teoremi\u2019ni 1995\u2019de kan\u0131tlayan Andrew Wiles, bu teoremle u\u011fra\u015fma s\u00fcrecini karanl\u0131k bir evde dola\u015fmaya benzetir: \u201cEvin ilk odas\u0131na giriyorsun karanl\u0131k. Kapkaranl\u0131k. E\u015fyalara \u00e7arpa \u00e7arpa, t\u00f6kezleyerek dola\u015f\u0131yorsun. Ama giderek neyin nerede oldu\u011funu \u00f6\u011freniyorsun. En nihayet alt\u0131 ay filan sonra, elektrik d\u00fc\u011fmesini buluyorsun, a\u00e7\u0131nca birden her \u015fey ayd\u0131nlan\u0131veriyor. Evi dola\u015fmaya devam ediyorsun, s\u0131ra bir sonraki karanl\u0131kodaya geliyor. Karanl\u0131kta bir alt\u0131 ay daha, yani at\u0131lan her \u00f6nemli ad\u0131m, bazen sadece bir an, bazen de belki birka\u00e7 g\u00fcn s\u00fcrm\u00fc\u015f bile olsa, daha \u00f6nce karanl\u0131kta ge\u00e7en aylar\u0131n bir sonucudur, ancak onlar sayesinde vard\u0131r.\u201d<\/p>\n
Andrew Wiles matematiksel ara\u015ft\u0131rma s\u00fcrecini anlat\u0131yor, ama karanl\u0131k ev benzetmesinde \u201cMatematik nas\u0131l \u00f6\u011frenilir?\u201d sorusunun yan\u0131t\u0131n\u0131 da bulmak m\u00fcmk\u00fcn. Matemati\u011fi \u00f6\u011frenmek i\u00e7in neler gerekir? D\u00f6rt temel \u015fey: Kitaplar, k\u00e2\u011f\u0131t, kalem ve bir oda.Yaln\u0131z kalarak, kendi sarmal\u0131nda d\u00f6ne d\u00f6ne, sab\u0131rla anlamaya \u00e7al\u0131\u015fmak.Odan\u0131n karanl\u0131\u011f\u0131ndan korkmadan,yarat\u0131c\u0131 akl\u0131n yakaca\u011f\u0131 \u0131\u015f\u0131\u011fa inanarak \u00e7abalamak. Ger\u00e7ek d\u00fcnyadan kopup, matemati\u011fin d\u00fcnyas\u0131nda ke\u015ffederek sonuca ula\u015fmak.<\/p>\n
\u0130zleyerek matematik yap\u0131lamayaca\u011f\u0131n\u0131n fark\u0131nda olmayan \u00e7o\u011fu ki\u015fi, matemati\u011fi \u00f6\u011fretmenden \u00f6\u011frenece\u011fini d\u00fc\u015f\u00fcn\u00fcr, oysa \u00f6\u011fretmeni dinleyerek sadece \u00f6\u011frendi\u011fimizi zannederiz (!), as\u0131l \u00f6\u011frenme kendi ba\u015f\u0131m\u0131za \u00e7\u0131k\u0131lan yolculukta ger\u00e7ekle\u015fir. Kendi d\u00fc\u015f\u00fcnme s\u00fcre\u00e7lerimizle oday\u0131 ayd\u0131nlatma \u00e7abas\u0131n\u0131 Cahit Arf b\u00fcy\u00fck harflerle \u201cANLAMAK\u201d diye yazm\u0131\u015ft\u0131r. E\u011fitmen,\u201cNas\u0131l?\u201d ve \u201cNeden?\u201d sorular\u0131n\u0131n yan\u0131tlar\u0131n\u0131 vermi\u015f olsa bile, bizim as\u0131l anlad\u0131\u011f\u0131m\u0131z an elektrik d\u00fc\u011fmesine ula\u015ft\u0131\u011f\u0131m\u0131z \u201caha!\u201d an\u0131d\u0131r.<\/p>\n
Odan\u0131n i\u00e7indeki e\u015fyalara \u00e7arparak, d\u00fc\u015fe kalka ilerlemek kolay de\u011fildir, ama \u00f6d\u00fcl\u00fc \u00e7ok b\u00fcy\u00fckt\u00fcr. Ufkumuz a\u00e7\u0131l\u0131r, ke\u015ffetti\u011fimiz \u015fey, ula\u015ft\u0131\u011f\u0131m\u0131z sonu\u00e7 art\u0131k bizimdir, bize aittir. Nerede kar\u015f\u0131m\u0131za \u00e7\u0131karsa \u00e7\u0131ks\u0131n hemen tan\u0131r, bu sayede di\u011fer karanl\u0131k odalarda daha cesurca dola\u015f\u0131r\u0131z.<\/p>\n
Sab\u0131rla anlamaya \u00e7al\u0131\u015farak al\u0131nacak \u00f6d\u00fcl i\u00e7in basit bir \u00f6rnek geliyor akl\u0131ma: Matematik yetenekleri birbirlerine denk iki \u00f6\u011frenciye a\u015fa\u011f\u0131daki iki sayma problemini sordu\u011fumuzu varsayal\u0131m.<\/p>\n
Birinci Problem.Sekiz \u00f6zde\u015f kalem \u00fc\u00e7 ki\u015fiye ka\u00e7 farkl\u0131 \u015fekilde da\u011f\u0131t\u0131labilir?<\/p>\n
\u0130kinci Problem. a,b,cnegatif olmayan tam say\u0131lar olmak \u00fczere<\/p>\n
a+b+c=8<\/p>\n
e\u015fitli\u011fini sa\u011flayan ka\u00e7 farkl\u0131 (a,b,c) \u00fc\u00e7l\u00fcs\u00fc vard\u0131r?<\/p>\n
Birbirlerinin benzeri olan bu problemlerin \u00e7\u00f6z\u00fcm\u00fc i\u00e7in gereken bilgi lise matemati\u011findeki Tekrarl\u0131 Perm\u00fctasyon form\u00fcl\u00fcd\u00fcr. Her iki \u00f6\u011frenciye de bu form\u00fcl\u00fc \u00e7\u0131kar\u0131l\u0131\u015f\u0131n\u0131 g\u00f6stererek verelim. \u00d6\u011frencilerden birine birinci problemi Tekrarl\u0131 Perm\u00fctasyon form\u00fcl\u00fcn\u00fcn uygulamas\u0131 olarak \u00e7\u00f6zelim, di\u011ferinden ayn\u0131 problemi, form\u00fcl\u00fc kullanarak \u00e7\u00f6zmesini isteyelim, yani ilkinde \u0131\u015f\u0131\u011f\u0131 biz yakal\u0131m, di\u011fer \u00f6\u011frenciyi ise \u201ckaranl\u0131k odaya\u201d g\u00f6nderelim. \u0130kinci \u00f6\u011frencinin birinci problemi \u00e7\u00f6zd\u00fc\u011f\u00fcn\u00fc varsayal\u0131m. Bu durumda ikincinin birinciye g\u00f6re ikinci problemi \u00e7\u00f6zme olas\u0131l\u0131\u011f\u0131 daha y\u00fcksektir; \u00e7\u00fcnk\u00fc daha \u00f6nceki soruda elektrik d\u00fc\u011fmesini kendi ba\u015f\u0131na bulmu\u015ftur. E\u011fer ikinci \u00f6\u011frenci birinci problemi \u00e7\u00f6zememi\u015f ve \u00e7\u00f6z\u00fcm\u00fc biz anlatm\u0131\u015fsak, yine de ikinci problemi \u00e7\u00f6zme olas\u0131l\u0131\u011f\u0131 daha fazlad\u0131r; \u00e7\u00fcnk\u00fc \u201ckaranl\u0131k odada\u201d\u00a0 kalarak \u00e7ok \u015fey kazanm\u0131\u015ft\u0131r ve \u201cYine dene, yine yenil, daha iyi yenil\u201d s\u00f6z\u00fcndeki \u201cdaha iyi yenilendir\u201d. Sonu\u00e7ta, her iki durumda da emek ve \u00e7abas\u0131n\u0131n kar\u015f\u0131l\u0131\u011f\u0131 olan \u00f6d\u00fcl\u00fc al\u0131r.<\/p>\n
Yukar\u0131daki \u00f6rne\u011fi bir kurguymu\u015f gibi anlatt\u0131m, ama asl\u0131nda y\u0131llard\u0131r kar\u015f\u0131la\u015ft\u0131\u011f\u0131m ger\u00e7ek bir olayd\u0131. \u0130lk kez,ikinci problemi \u00e7\u00f6zen bir \u00f6\u011frencimin birinci problemi de kendi kendine \u00e7\u00f6zd\u00fc\u011f\u00fcn\u00fc \u00f6\u011frendi\u011fimde akl\u0131ma gelmi\u015fti bu \u201coyunu\u201d farkl\u0131 \u00f6\u011frencilerle de oynamak. Matematik yetenekleri farkl\u0131 birka\u00e7 \u00f6\u011frenci d\u0131\u015f\u0131nda yukar\u0131da yazd\u0131\u011f\u0131m gibi hep birinci problemin \u00e7\u00f6z\u00fcm\u00fcn\u00fc kendi ke\u015ffeden \u00f6\u011frencilerin ikinci problemi de kolayl\u0131kla \u00e7\u00f6zd\u00fc\u011f\u00fcne tan\u0131k oldum.<\/p>\n
Matemati\u011fin ne denli ayd\u0131nl\u0131k bir d\u00fcnyas\u0131 oldu\u011funu \u00e7ok iyi biliyoruz, ama matematik \u00f6\u011frenmek, ayd\u0131nl\u0131\u011fa ula\u015fmak i\u00e7in karanl\u0131kta dola\u015fmay\u0131 da g\u00f6ze almay\u0131 gerektiriyor. Belki de t\u00fcm d\u00fcnyada matematik \u00f6\u011fretiminde ya\u015fanan onca s\u0131k\u0131nt\u0131 herkesten bu cesareti ve \u00e7abay\u0131 beklemekten kaynaklan\u0131yor.<\/p>\n
Not: Yaz\u0131da s\u00f6z\u00fc edilen Tekrarl\u0131 Perm\u00fctasyon form\u00fcl\u00fcn\u00fc ve verdi\u011fimiz problemlerin \u00e7\u00f6z\u00fcm\u00fcn\u00fc, ilgin\u00e7 ve e\u011flenceli di\u011fer baz\u0131 problemlerle birlikte gelecek say\u0131da ele alaca\u011f\u0131z.<\/p>\n","protected":false},"excerpt":{"rendered":"
\u00dc\u00e7 y\u00fcz elli y\u0131l boyunca \u00e7\u00f6z\u00fclmemi\u015f Fermat\u2019\u0131n Son Teoremi\u2019ni 1995\u2019de kan\u0131tlayan Andrew Wiles, bu teoremle u\u011fra\u015fma s\u00fcrecini karanl\u0131k bir evde dola\u015fmaya benzetir: \u201cEvin ilk odas\u0131na giriyorsun karanl\u0131k. Kapkaranl\u0131k. E\u015fyalara \u00e7arpa \u00e7arpa, t\u00f6kezleyerek dola\u015f\u0131yorsun. Ama giderek neyin nerede oldu\u011funu \u00f6\u011freniyorsun. En nihayet alt\u0131 ay filan sonra, elektrik d\u00fc\u011fmesini buluyorsun, a\u00e7\u0131nca birden her \u015fey ayd\u0131nlan\u0131veriyor. Evi dola\u015fmaya […]<\/p>\n","protected":false},"author":375,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[160,38,514,510],"tags":[3562,208],"class_list":["post-27161","post","type-post","status-publish","format-standard","hentry","category-123-sayi","category-dergi-sayilari","category-matematik-sohbetleri","category-surekli-bolumler","tag-ali-torun","tag-matematik"],"acf":[],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t